I’ve been making my way through the text, Mathematics for Human Flourishing by Frances Su and Christopher Jackson. At first, as I read his claims and poked a bit at the math, my response was my usual: I like algebra because it is neat and tidy and, best of all, you can check your own work! It’s a closed system that eliminates pesky guessing and rewards precision. But there is no “play” for me in math, just the satisfaction of a completed and well done exercise.
Su’s contention is that we need to play with the math. I had been feeling pretty left out of that claim, until I realized that I was thinking about my lunch in terms of math….
I had soup for lunch yesterday. I ate it in a round bowl that has sloped sides.
Each time I took one spoonful out of the bowl it was, within the constraints of mathematical modeling, about the same volume as all the other spoonfuls, give or take a tomato chunk.
However, while the amount removed in each spoonful may have been (virtually) equivalent to the amount removed in the other spoonfuls, the depth of the soup remaining in the bowl changed by a different amount with each spoonful, due to the shape of the bowl, specifically, the sloped sides.
Thinking about this made me remember calculus, where we took slices on a coordinate plane and sliced them thinner and thinner, infinitely thinner, while also adding them up to determine the area under the curve. My “slices” of soup were not particularly thin; in fact, I suspect they got “fatter” as I moved towards the bottom of the bowl, where a spoonful of soup brought the level down more than an earlier spoonful.
With Su in mind, I started to wonder about what questions could I ask from this experience. What would I call the shape of each soup slice, since the tops and bottoms were circles but the heigh was slanted and the circles were different sizes, like a cross between a trapezoid and a circle? Could I represent the situation algebraically? Would I need calculus, which measures change, or was it discrete? What would I need to do as a teacher to encourage students to play mathematically?
It has been a long couple of months, more like over a year, since I’ve had the time or mental stamina to do any thinking just for its own sake or for the satisfaction of wondering. I didn’t answer my own question, but I’m re-inspired to think about how to support my students in getting to a place where they can see math as an option for exploration.
“Low performance should not be used as an excuse to rob students of opportunity.” (Su, F. & Jackson, C., Mathematics from Human Flourishing, pg. 156)